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IMA Journal of Mathematical Control and Information 1990 7(1):35-45; doi:10.1093/imamci/7.1.35
© 1990 by Institute of Mathematics and its Applications
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A Note on a System Theoretic Approach to a Conjecture by Peller-Khrushchev: The General Case

RAIMUND OBER

Department of Engineering, University of Cambridge Trumpington Street, Cambridge CB2 1PZ, UK

Based on the construction of infinite-dimensional balanced realizations, an alternative solution to the following inverse spectral problem is presented. Given a decreasing sequence of positive numbers ({sigma}n)n>1 (i.e. {sigma}1≥{sigma}2≥{sigma}3≥...≥0), does there exist a Hankel operator whose sequance of singular values is ({sigma}n)n>1? This paper is an extension of a previously published paper in which the same approach was taken in the case of a monotonically decreasing sequence({sigma}n)n>1.


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